Non-deterministic genotype-phenotype maps of biological self-assembly^(a)

¹ Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge - JJ Thomson Avenue, CB3 0HE Cambridge, UK
² Sainsbury Laboratory, University of Cambridge - Bateman Street, CB2 1LR Cambridge, UK

Received: 1 June 2018
Accepted: 14 August 2018

Abstract

In recent years large-scale studies of different genotype-phenotype (GP) maps, including those of RNA secondary structure, lattice proteins, and self-assembling Polyominoes, have revealed that these maps share structural properties. Such properties include skewed distributions of genotypes per phenotype, negative correlations between genotypic evolvability and robustness, positive correlations between phenotypic evolvability and robustness, and the fact that a majority of phenotypes can be reached from any genotype in just a few mutations. Traditionally this research has focused on deterministic GP maps, meaning that a single sequence maps to a single outcome. Here, by contrast, we consider non-deterministic GP maps, in which a single sequence can map to multiple outcomes. Most GP maps already contain such sequences, but these are typically classified as a single, undesirable phenotype for the reason that biological processes typically rely on robust transformation of sequences into biological structures and functions. For the same reason, however, non-deterministic phenotypes play an important role in diseases, and a deeper understanding of non-deterministic GP maps may therefore inform the study of their evolution. By redefining deterministic and non-deterministic Polyomino self-assembly phenotypes in terms of the pattern of possible interactions rather than the final structure we are able to calculate GP map properties for the non-deterministic part of the map, and find that they match those found in deterministic maps.